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Out of 200 grade 12 students, 108 are taking Natural Math and 115 are taking Managesial Math. If 54 are taking neither, how many are taking both? How many are taking either but not both?

Answers

Given:
total number of students = 200
total number of students taking Natural math = 108
total number of students taking Managesial math = 115
total number of students taking neither = 54
Required:
number of students taking both math subjects
number of students taking either but not both
Solution:
let x be the number of students taking both
let y be the number of students taking nat. math
let z be the number of students taking man. math
y = (total n of students - n of students taking nat. math) - n of students taking neithe
y = (200 - 108) - 54
y = 31
z = (total n of students - n of students taking man. math) - n of students taking neither
z = (200 - 115) - 54
z = 38
x = (108 - y) or x = (115 - z)
x = 77